A temporal fixpoint calculus

  • Authors:

  • M. Y. Vardi

  • Affiliations:

  • IBM Almaden Research Center

  • Venue:
  • POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 1988

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Abstract

Two distinct extensions of temporal logic has been recently advocated in the literature. The first extension is the addition of fixpoint operators that enable the logic to make assertions about arbitrary regular events. The second extension is the addition of past temporal connectives that enables the logic to refer directly to the history of the computation. Both extensions are motivated by the desire to adapt temporal logic to modular, i.e., compositional, verification (as opposed to global verification). We introduce and study here the logic &mgr;TL, which is the extension of temporal logic by fixpoint operators and past temporal connectives. We extend the automata-theoretic paradigm to &mgr;TL. That is, we show how, given an &mgr;TL formula @@@@, we can produce a finite-state Büchi automaton A@@@@, whose size is at most exponentially bigger than the size of @@@@, such that A@@@@ accepts precisely the computations that satisfy @@@@. The result has immediate applications, e.g., an optimal decision procedure and a model-checking algorithm for &mgr;TL.